recategorized by
418 views
0 votes
0 votes

If $x$ is real, the set of real values of $a$ for which the function $$y=x^2-ax+1-2a^2$$ is always greater than zero is

  1. $- \frac{2}{3} < a \leq \frac{2}{3}$
  2. $- \frac{2}{3} \leq  a < \frac{2}{3}$
  3. $- \frac{2}{3} < a < \frac{2}{3}$
  4. None of these
recategorized by

1 Answer

1 votes
1 votes

Refer this on how to use discriminant to solve such problems.

For the quadratic function  $ax^{2}+bx+c=0$ to have positive value, the discriminant $b^{2}-4ac<$  $0$

So, on simplifying for the given function, we get   $9$$a^{2}$ $<$ $4$  $\Rightarrow$  $a^{2}$  $<$  $\frac{4}{9}$  $\Rightarrow$  $-\frac{2}{3}$  $<$ $a$  $<$  $\frac{2}{3}$

Option C is the answer.

Related questions

2 votes
2 votes
2 answers
1
Arjun asked Sep 23, 2019
507 views
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is$-15$$22$$11$$0$
2 votes
2 votes
3 answers
2
Arjun asked Sep 23, 2019
558 views
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1 , \sqrt{3}{/2}]$the interval $[-\sqrt{3}{/2}, 1]$the interval $[-1, 1]$none of...
1 votes
1 votes
1 answer
3
Arjun asked Sep 23, 2019
459 views
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$....
0 votes
0 votes
1 answer
4
Arjun asked Sep 23, 2019
410 views
Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true.For all real $y$, there exists $x$ such that $f(x)=y$For all real $y \neq 1$, ...